Since, somewhat surprisingly, mostly chiral exotic leptons are not yet ruled-out,
it would be interesting to see
the potential implications of the setup discussed in this paper
on the physics of light vectors coupled to anomalous currents.
The most relevant application turns out to be for the case of electro-phobic
light vectors (\(\alpha _e = 0\)  in Eq. (REF )),
for which the bounds stemming from WZ terms are typically the most important ones.
These include, for instance, baryonic forces (\(\alpha _B \ne 0\) )
which have a rich
accelerator and collider phenomenology (see e.g. [1]}, [2]}),
while a case motivated by the \(g\) -2 anomaly [3]} is that of
purely muonic forces (\(\alpha _\mu \ne 0\) ) which are in principle
distinguishable from more standard scenarios based on
\({\rm U}(1)_{\mu - \tau }\)  (see e.g. [4]}).
The general framework discussed in Sect.  provides a consistent
UV completion for light vectors coupled to anomalous SM fermionic currents, allowing to free large portions of parameter space from the bounds of
Ref. [5]}, [6]}, until the HL-LHC will give the final word on the existence of
mostly chiral exotic leptons.
